Serco has already agreed to repay £70 million plus VAT, meaning the full amount reimbursed by the two firms will top £214 million.

G4S’s settlement represented a significant increase on its earlier offer of £24.1 million, which wasrejected by the MoJ.

Mr Grayling told MPs: “G4S has agreed to repay £108.9 million plus VAT to reimburse the government for overpayments made by my department under the electronic monitoring contract and to cover direct costs to government arising from these issues.

“This sum also includes £4.5 million to cover the cost of overpayments made on two contracts held by G4S for facilities management in the courts, both of which were referred to the Serious Fraud Office in December.

“I am satisfied ... that this represents a good deal for the taxpayer. In the event of criminal charges being brought we would consider whether further sums are due from G4S.”

An inquiry was launched in May after it emerged that G4S and Serco had been overcharging the taxpayer for electronic tagging offenders.

In some cases, the government had been spuriously billed for tagging criminals who had absconded, been sent back to prison, or who had died.

G4S is still in discussions with the Cabinet Office over its ability to bid for new government contracts.

It showed G4S billed the taxpayer £4,700 for monitoring an offender even though equipment had been removed 935 days earlier, and it charged for 612 days’ tagging - at a cost of £3,000 - even though it had been informed the offender had been sent to prison and the company had removed the monitoring equipment from his home.

Sadiq Khan, the shadow justice secretary, said: "This large sum of money G4S are repaying taxpayers shows the true scale of the wrongdoing that went on.

"This, in addition to its poor performance on a number of other contracts, has led to huge damage to the public’s confidence in our criminal justice system.

“However, it is not for G4S to feel it can just wipe the slate clean. The Serious Fraud Office is still investigating, and G4S should be treated in just the same way as any member of the public would, with no special cosy deals between the Tory-led Government and big business.”